A342025 a(n) = 1 if n has the same numbers of prime factors of forms 4*k+1 and 4*k+3 when counted with multiplicity, otherwise 0.

1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Mathematica

{1}~Join~Table[Boole[Count[#, 1] == Count[#, 3]] &@ Mod[Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[n]], 4], {n, 2, 120}] (* Michael De Vlieger, Mar 11 2021 *)

Prog

(PARI) A342025(n) = {my(f = factor(n)); sum(k=1, #f~, ((f[k, 1] % 4)==1)*f[k, 2]) == sum(k=1, #f~, ((f[k, 1] % 4)==3)*f[k, 2]); }; \\ From isok function in A072202
(Python)
from sympy import factorint
def A342025(n):
    f = factorint(n)
    return int(sum(b for a, b in f.items() if a % 4 == 3) == sum(b for a, b in f.items() if a % 4 == 1)) # Chai Wah Wu, Mar 09 2021

Crossrefs

Characteristic function of A072202.

Sequence in context: A036987 A354193 A354188 * A353518 A353687 A354918

Adjacent sequences: A342022 A342023 A342024 * A342026 A342027 A342028

Keyword

nonn

Author

Antti Karttunen, Mar 09 2021

Status

approved